MAT222: Intermediate Algebra

Professor Andrea Grych

Assignment 4: Real World Quadratic Functions

Managers and business people use quadratic equations on a daily basis in order to find out how much of a profit can be made. The following problem is an example of that. On page number 666 of the textbook, problem number 56 (Dugopolski, 2012) states that in order to get maximum profits, a chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?

In order to solve the first question of what number of clerks will maximize the profit, the function -25x + 300x = 0 must be solved in order to get the x-intercepts of the parabola.

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25x2 – 300x = 0 Factor the left side of the problem.

25x (x – 12) = 0 Now use the Zero Factor Property.

25x = 0 or x – 12 = 0 Solve each problem. x = 0 or x = 12 This means that the parabola will cross the x-axis at 0 and 12.

Now that we know where the parabola will cross the x –axis at, the next question can be asked. What number of clerks will maximize the profit?

-b / (2a) This is the formula that will be used.

-300 / 2(-25) Solve

-300 / -50

6 6 clerks will maximize the